BPS invariants from p-adic integrals

2021/12/22 by Francesca Carocci, Carocci, Francesca, Giulio Orecchia +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.12103

openalex publication_date 2021/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define p-adic BPS or pBPS-invariants for moduli spaces M_β,χ of 1-dimensional sheaves on del Pezzo surfaces by means of integration over a non-archimedean local field F . Our definition relies on a canonical measure μ_can on the F-analytic manifold associated to M_β,χ and the pBPS-invariants are integrals of natural \mathbbG_m-gerbes with respect to μ_can. A similar construction can be done for meromorphic Higgs bundles on a curve. Our main theorem is a χ-independence result for these pBPS-invariants. For 1-dimensional sheaves on del Pezzo surfaces and meromorphic Higgs bundles, we obtain as a corollary the agreement of pBPS with usual BPS-invariants trough a result of Maulik-Shen.

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